Question

the exterior angle of a regular polygon measures 20°. how many sides does the polygon have?

Explanation:

Step1: Recall the formula

The sum of exterior angles of any polygon is $360^{\circ}$. For a regular polygon, all exterior - angles are equal. Let $n$ be the number of sides of the polygon and $x$ be the measure of each exterior angle. Then the formula is $n=\frac{360^{\circ}}{x}$.

Step2: Substitute the given value

We are given that $x = 20^{\circ}$. Substituting $x = 20^{\circ}$ into the formula $n=\frac{360^{\circ}}{x}$, we get $n=\frac{360}{20}$.

Step3: Calculate the value of $n$

$\frac{360}{20}=18$.

Answer:

18